Challenge to the 1st postulate

Does the fact that a car burns fuel to keep it moving mean that we can truely say that the car is moving and not the earth? If so does this disprove the 1st postulate that maintains ALL uniform motion is relative?

*I know that objects in space dont require fuel to move at a constant speed relative to the solar system- but I am specifically interested in situations on earth where frictional forces do matter.

In special relativity, the first postulate does not apply. To get (or, with friction present, even keep) the car moving at some final velocity v, it needs to accelerate relative to the ground. This is easily measurable (just suspend a mass from a string and measure the angle to the vertical).

In general relativity, IIRC, there is no claim that accelerating observers are equivalent. GR just says that uniform acceleration is indistinguishable from constant motion in a gravitational field. Since speeding up or braking in a car produces an acceleration in directions perpendicular to gravity, that people outside cars do not feel, we are inclined to say that there is no gravitational field along the surface of the planet but the car itself is accelerating w.r.t. the ground.

Does the fact that a car burns fuel to keep it moving mean that we can truely say that the car is moving and not the earth? If so does this disprove the 1st postulate that maintains ALL uniform motion is relative?

No. Let's say the car is moving at a constant velocity of 60 mph to the east. There is nothing wrong with describing the relative motion from the perspective of the car. The wind and Earth are moving 60 mph to the west from this perspective. This wind blowing to the west and westward moving Earth result in frictional forces on the (stationary) car. The car needs to apply forces to the road, and hence back to itself via Newton's third law, to keep the net force on the car zero.